Intergrating Ticketing systems into company website

We are building a new WordPress website (previously built using Dreamweaver) as our company facing website, we also use Jira hosted on the cloud as our ticketing system. I see there are several ticketing plugins for WordPress and wondering if we should put all our eggs into on basket so to speak. We are happy with Jira (but it is probably over complicated for our needs).
Id appreciate peoples opinions on weather or not its a good idea to combine the two systems or keep them separate.